#!/usr/bin/python
# 
# The quadratic cone program of section 8.2 (Quadratic cone programs).
  
# minimize   (1/2)*x'*A'*A*x - b'*A*x
# subject to x >= 0
#            ||x||_2 <= 1

from cvxopt import matrix, base, solvers
A = matrix([ [ .3, -.4,  -.2,  -.4,  1.3 ], 
             [ .6, 1.2, -1.7,   .3,  -.3 ],
             [-.3,  .0,   .6, -1.2, -2.0 ] ])
b = matrix([ 1.5, .0, -1.2, -.7, .0])
m, n = A.size

I = matrix(0.0, (n,n))
I[::n+1] = 1.0
G = matrix([-I, matrix(0.0, (1,n)), I])
h = matrix(n*[0.0] + [1.0] + n*[0.0])
dims = {'l': n, 'q': [n+1], 's': []}
x = solvers.coneqp(A.T*A, -A.T*b, G, h, dims)['x']
print "\nx = \n\n", x